How can I implement runge kutta method to a control problem in Simulink ?

Hello Everyone,

I have a question about the implementation of the Runge Kutta method in a control system. I have used a general inverted pendulum problem with a PID controller. What I want to achieve is trying to write my Runge Kutta code and compare it with Simulink ode4 solver. The point that I am stuck is the implementation of Runge Kutta with a control input. The general version of Runge Kutta shows only half and one time step ahead with state variables of ODE. However, in a control problem, you need to calculate the control input at and where h is time step. Somehow Simulink handles this problem and I couldn't find how Simulink calculates and approximates future control input values.

I have tried to calculate one step ahead control input and interpolate the control input value between and . The results are quite similar but they don't coincide with each other. I have shared the results below.

Could you please help me, how should we implement the control input to calculate in advance in the Runge-Kutta method? And Do you have knowledge about how Simulink calculates and implement control input when we select the ode4 solver selection?

[Sam Chak]

I don't see the mathematical formula for the PID input. Maybe that caused the problem?

[Dogan Yildiz]

What I want to ask is a general problem actually. How can we handle the input variable during Runge-Kutta solver ? We need future input at that time instant, so we need to determine the future input to solve a differential equation with an input variable. In our case, this input comes to differential equation from a controller. In that case, how we treat and solve future input and what is the Simulink approach to handle the problem ? These are my questions. Thanks for the reply, by the way :)

[Kristof]

I have the same problem, I am looking for a general soulution to this situation. I tried to do the following: I took the derivative of the input force (from the current and the previous value), and predicted the future by that. But it is tricky, that my PID evaulates a new input force by its own selfprediction?

[Yuichiro Aoyama]

I am not sure if this is answering the question, but in the vido below, the same u(t) is used all over the integration interval and works well.

https://www.youtube.com/watch?v=OOL5Mo_jYGY